Measuring transitional matrix elements using first-order perturbation theory in Coulomb excitation

Abstract

The aim of nuclear structure physics is to study the interplay between singleparticle and collective degrees of freedom in nuclei and to explain how nuclei get excited and decay under di erent external conditions, such as strong electric and magnetic elds. If nuclei absorb a large amount of energy and angular momentum, like in a scattering reaction when you bombard a target that is in the ground state with a projectile at high bombarding energies, the energy from the projectile gets transfered to the target and vice versa, hence both projectile and target may get excited. During the de-excitation process nuclei may release the energy in a form of electromagnetic radiation (gamma rays) which carries angular momentum. The atomic nucleus is a many-body system, whose structure is de ned in terms of interactions between protons and neutrons. In nature there are only around 300 stable isotopes [1]. They are all in their ground states (although some are in a low-energy excited isomeric state with a long lifetime). To study excited states in these nuclei one needs to provide energy to the system. In addition, there are some 3000 unstable nuclei, most of which do not exist in nature. Many have been produced and studied in research laboratories, and there could be more than 3000 other unstable nuclei that can in principle exist in astrophysical environments, but have not yet been synthesized on Earth [1].